1. Jump to first page 1 Mechanics AP200 Dr. C. W. Ong Meriam, J.L., Kraige, L.G., “Engineering Mechanics, Dynamics”, John Wiley Course Work 30% (Exercises and tests) Examination 70% Download materials http://ap.polyu.edu.hk/apacwong/

2. Jump to first page 2 Chapter 1 Vector A vector has a length A and a direction (unit vector ) A

3. Jump to first page 3 2D Cartesian coordinate system (one form of presentation) x y  Pythagoras theorem

4. Jump to first page 4 3-D Cartesian coordinate system z x y AyAy AxAx AzAz

5. Jump to first page Addition of vectors y x O Subtraction of vectors y x O

6. Jump to first page 6 Dot (scalar) product of two vectors In 2-D Cartesian coordination system Definition: Note: AB cos  = AB cos (  A -  B ) = AB(cos  A cos  B +sin  A sin  B ) = (Acos  A )(Bcos  B ) + (Asin  A ) (Bsin  B ) x y

7. Jump to first page 7 y O  From cosine law: In 3-D Cartesian coordinate system: x

8. Jump to first page 8 Application of dot product: Projection Area A A’  a l = l a Projected area = = l a cos  

9. Jump to first page 9 Exercise: Find the projection of vector with a length of 10 unit along. 60 o 30 o

10. Jump to first page 10 Cross product i k j

11. Jump to first page 11 x y

12. Jump to first page 12 In Cartesian coordinate system: